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A student wants to know what is wrong with the following “proof” that
Let
Butalso
Thus,
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- 32 Probability and Statistics: Bayes' Theorem Task: Refer to Question 32 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward30 Functional Analysis: Banach Spaces Task: Refer to Question 30 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward4 5 Riemannian Geometry: Geodesics Task: Refer to Question 45 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward
- 31 Vector Calculus: Divergence Theorem Task: Refer to Question 31 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward41 Algebraic Geometry: Affine and Projective Varieties Task: Refer to Question 41 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing 42 Fourier Transform: Applications to Signal Processing Task: Refer to Question 42 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward2 4 Partial Differential Equations: Method of Separation of Variables Task: Refer to Question 24 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward
- 31 Vector Calculus: Divergence Theorem Task: Refer to Question 31 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing 32 Probability and Statistics: Bayes' Theorem Task: Refer to Question 32 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC44OAZF/view?usp=sharingarrow_forward7. Rank and Nullity: 1 2 1 Let A - 2 4 2 a) Find the rank of matrix A. 3 6 3 b) Find the nullity of matrix A. c) Show that the rank-nullity theorem holds for matrix A. 8. Change of Basis: Consider the vector space R² with the standard basis {e1 = (1,0), e2 = (0, 1)} and a new basis {v1 = (1, 1), V2 = (1, −1)}. a) Find the change of basis matrix from the standard basis to the new basis. b) Express the vector w = (2, 3) in the new basis {V1, V2}.arrow_forward26 Numerical Methods: Newton-Raphson Method Task: Refer to Question 26 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward
- - Let V = R4, and let the set S = {(1, 2, 3, 4), (0, 1, 2, 3), (0, 0, 1, 2)} be a subset of V. a) Show that S is linearly independent. b) Find the dimension of the subspace spanned by S. c) Find a basis for the orthogonal complement of the subspace spanned by S.arrow_forwardLet A be a 4 x 4 matrix with the following characteristic polynomial: a) Find the eigenvalues of A. P(A) = 46A3 + 11λ² – 6A b) Find the geometric multiplicity of each eigenvalue. c) Determine the diagonalizability of A.arrow_forward43 Game Theory: Nash Equilibrium Task: Refer to Question 43 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing 44 Tensor Calculus: Covariant and Contravariant Tensors Task: Refer to Question 44 in the provided document. Link: https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharingarrow_forward
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